Finite Group Databasebeta

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C7×C11×Dic57 #31798199

order17556
isoclinismisoclinic class of D57
automorphism?
homologyAbelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×Dic57
unambiguous semidirect productC3⋊(C7×C11×Dic19)
unambiguous semidirect productC19⋊(C7×C11×Dic3)

Splittings

derived, HallC3×C19 ⋊ C4×C7×C11
HallC3×C7×C11×C19 ⋊ C4
HallC7×C11×C19 ⋊ Dic3
HallC3×C11×C19 ⋊ C4×C7
HallC3×C7×C19 ⋊ C4×C11
HallC3×C7×C11 ⋊ Dic19
HallC11×C19 ⋊ C7×Dic3
HallC7×C19 ⋊ C11×Dic3
HallC3×C11 ⋊ C7×Dic19
HallC3×C7 ⋊ C11×Dic19
SylowC19 ⋊ C7×C11×Dic3
SylowC3 ⋊ C7×C11×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11D57
commutator, hypocenterC3×C19C4×C7×C11
FrattiniC2C7×C11×D57
Fitting, socle, prime radicalC2×C3×C7×C11×C19C2
cosocleC2×C3×C19C2×C7×C11
LCSG ▷ C3×C19
UCSC1 ◁ C2×C7×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17556

Conjugacy classes & character table

4620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 14);